More Like this

1. Domain Generalization by Marginal Transfer Learning

   Blanchard, Gilles; Deshmukh, Aniket Anand; Dogan, Urun; Lee, Gyemin; Scott, Clayton (January 2021, Journal of machine learning research)

   null (Ed.)

   In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner. This problem arises in several applications where data distributions fluctuate because of environmental, technical, or other sources of variation. We introduce a formal framework for DG, and argue that it can be viewed as a kind of supervised learning problem by augmenting the original feature space with the marginal distribution of feature vectors. While our framework has several connections to conventional analysis of supervised learning algorithms, several unique aspects of DG require new methods of analysis. This work lays the learning theoretic foundations of domain generalization, building on our earlier conference paper where the problem of DG was introduced (Blanchard et al., 2011). We present two formal models of data generation, corresponding notions of risk, and distribution-free generalization error analysis. By focusing our attention on kernel methods, we also provide more quantitative results and a universally consistent algorithm. An efficient implementation is provided for this algorithm, which is experimentally compared to a pooling strategy on one synthetic and three real-world data sets. Keywords: domain generalization, generalization error bounds, Rademacher complexity, kernel methods, universal consistency, kernel approximation 

   more » « less
2. UNDERSTANDING WHY GENERALIZED REWEIGHTING DOES NOT IMPROVE OVER ERM

   Zhai, Runtian; Dan, Chen; Kolter, Zico; Ravikumar, Pradeep (May 2023, International Conference on Learning Representations)

   Empirical risk minimization (ERM) is known to be non-robust in practice to distributional shift where the training and the test distributions are different. A suite of approaches, such as importance weighting, and variants of distributionally robust optimization (DRO), have been proposed to solve this problem. But a line of recent work has empirically shown that these approaches do not significantly improve over ERM in real applications with distribution shift. The goal of this work is to obtain a comprehensive theoretical understanding of this intriguing phenomenon. We first posit the class of Generalized Reweighting (GRW) algorithms, as a broad category of approaches that iteratively update model parameters based on iterative reweighting of the training samples. We show that when overparameterized models are trained under GRW, the resulting models are close to that obtained by ERM. We also show that adding small regularization which does not greatly affect the empirical training accuracy does not help. Together, our results show that a broad category of what we term GRW approaches are not able to achieve distributionally robust generalization. Our work thus has the following sobering takeaway: to make progress towards distributionally robust generalization, we either have to develop non-GRW approaches, or perhaps devise novel classification/regression loss functions that are adapted to GRW approaches. 

   more » « less
3. Domain Generalization by Marginal Transfer Learning

   Blanchard, Gilles; Deshmukh, Aniket Anand; Dogan, Urun; Lee, Gyemin; Scott, Clayton (January 2021, Journal of machine learning research)

   In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner. This problem arises in several applications where data distributions fluctuate because of environmental, technical, or other sources of variation. We introduce a formal framework for DG, and argue that it can be viewed as a kind of supervised learning problem by augmenting the original feature space with the marginal distribution of feature vectors. While our framework has several connections to conventional analysis of supervised learning algorithms, several unique aspects of DG require new methods of analysis. This work lays the learning theoretic foundations of domain generalization, building on our earlier conference paper where the problem of DG was introduced (Blanchard et al., 2011). We present two formal models of data generation, corresponding notions of risk, and distribution-free generalization error analysis. By focusing our attention on kernel methods, we also provide more quantitative results and a universally consistent algorithm. An efficient implementation is provided for this algorithm, which is experimentally compared to a pooling strategy on one synthetic and three real-world data sets. 

   more » « less
4. Iterative Feature Matching: Toward Provable Domain Generalization with Logarithmic Environments

   Chen, Yining; Rosenfeld, Elan; Sellke, Mark; Ma, Tengyu; Risteski, Andrej (January 2022, Advances in neural information processing systems)

   Domain generalization aims at performing well on unseen test environments with data from a limited number of training environments. Despite a proliferation of proposed algorithms for this task, assessing their performance both theoretically and empirically is still very challenging. Distributional matching algorithms such as (Conditional) Domain Adversarial Networks [12, 28] are popular and enjoy empirical success, but they lack formal guarantees. Other approaches such as Invariant Risk Minimization (IRM) require a prohibitively large number of training environments—linear in the dimension of the spurious feature space ds—even on simple data models like the one proposed by Rosenfeld et al. [37]. Under a variant of this model, we show that ERM and IRM can fail to fnd the optimal invariant predictor with o(ds) environments. We then present an iterative feature matching algorithm that is guaranteed with high probability to find the optimal invariant predictor after seeing only O(log ds) environments. Our results provide the first theoretical justification for distribution-matching algorithms widely used in practice under a concrete nontrivial data model. 

   more » « less
5. Characterizing and Understanding the Generalization Error of Transfer Learning with Gibbs Algorithm

   Bu, Y; Arminian, G; Toni, L.; Wornell, G. W.; Rodrigues, M. R. (March 2022, Proceedings of Machine Learning Research)

   We provide an information-theoretic analy- sis of the generalization ability of Gibbs- based transfer learning algorithms by focus- ing on two popular empirical risk minimiza- tion (ERM) approaches for transfer learning, α-weighted-ERM and two-stage-ERM. Our key result is an exact characterization of the generalization behavior using the conditional symmetrized Kullback-Leibler (KL) informa- tion between the output hypothesis and the target training samples given the source train- ing samples. Our results can also be applied to provide novel distribution-free generaliza- tion error upper bounds on these two afore- mentioned Gibbs algorithms. Our approach is versatile, as it also characterizes the gener- alization errors and excess risks of these two Gibbs algorithms in the asymptotic regime, where they converge to the α-weighted-ERM and two-stage-ERM, respectively. Based on our theoretical results, we show that the ben- efits of transfer learning can be viewed as a bias-variance trade-off, with the bias induced by the source distribution and the variance induced by the lack of target samples. We believe this viewpoint can guide the choice of transfer learning algorithms in practice. 

   more » « less